Wavelet transform encoding method is known as one of the methods for high-efficiency encoding of two-dimensional signals represented by image signals.
In the wavelet transform encoding method, first, wavelet transform is applied to a two-dimensional signal. The wavelet transform is a kind of subband encoding, which results in N-hierarchy band division by repeating subband division at the low-frequency side for band division in horizontal and vertical directions, respectively. Such kind of band division is called octave division. In the case of division up to three hierarchies, 10 subbands are available as shown in FIG. 19.
In FIG. 19, F0 to F3 are subbands of the lowest hierarchy; F4 to F6 are subbands of the hierarchy thereabove; and F7 to F9 are subbands of the highest hierarchy. Further, F1, F4 and F7 are subbands filtered through a lowpass filter in a horizontal direction and through a highpass filter in a vertical direction; F2, F5 and F8 are subbands filtered through a highpass filter in a horizontal direction and through a lowpass filter in a vertical direction; and F3, F6 and F9 are subbands filtered through a highpass filter in both horizontal and vertical directions. Further, F0 is called the lowest-frequency subband and, other than F0, F1 to F9 are called high-frequency subbands.
A wavelet transform coefficient is included in each of the subbands F0 to F9. In the present description, a wavelet transform coefficient called LH is included in subbands such as F1, F4 and F7 filtered through a lowpass filter in the horizontal direction and through a highpass filter in the vertical direction. Further, a wavelet transform coefficient called HL is included in subbands such as F2, F5 and F8 filtered through a highpass filter in the horizontal direction and through a lowpass filter in the vertical direction. Further, a wavelet transform coefficient called HH is included in subbands such as F3, F6 and F9 filtered through a highpass filter in both the horizontal and vertical directions. Further, a wavelet transform coefficient called LL is included in the lowest-frequency subband F0. Furthermore, the same coordinates are assigned to the wavelet transform coefficients LH, HL and HH of the same spatial coordinates in a plurality of high-frequency subbands of the same hierarchy to be expressed, for example, as LH(i, j), HL(i, j) and HH(i, j). Therein, x represents the horizontal direction, and y represents the vertical direction; thus, the coordinates are expressed as (x, y).
When wavelet transform is carried out in the above manner, the electric power is inclined to the wavelet transform coefficient LL included in the lowest-frequency subband, and the wavelet transform coefficients LH, HL and HH included in the high-frequency subbands become approximately zero in value. Therefore, it is possible to compress the amount of information by utilizing variable-length codes, the code length of which becomes shorter as the value gets closer to zero, to encode the wavelet transform coefficients LH, HL and HH included in the high-frequency subbands. Further, because quantizing the wavelet transform coefficients LH, HL and HH increases the number of the wavelet transform coefficients of zero, it is possible to further highly compress the amount of information by concomitantly utilizing run length compression or encoding.
Herein, as methods for encoding the wavelet transform coefficients included in the high-frequency subbands, there are a method of respectively encoding LH, HL and HH such as JPEG2000 (ISO-15444-1/ITU-T Rec. 800), and a method of grouping LH, HL and HH located spatially at the same position within a plurality of subbands belonging to the same hierarchy and encoding for each group as shown in Patent Documents 1 and 2 and Non-Patent Document 1. The present invention relates to improvement of the latter method.
On the other hand, in wavelet transform decoding, the original two-dimensional signal is generated by inputting the code string created by wavelet transform encoding, and following the procedure opposite to the encoding.
The method of encoding by grouping LH, Hl and HH located spatially at the same position within the LH subband, HL subband and HH subband belonging to the same hierarchy is further classified roughly into: a method of individually encoding the plurality of wavelet transform coefficients included in the group (hereinafter, referred to as the individual coefficient encoding method); and a method of collectively encoding the plurality of wavelet transform coefficients included in the group (hereinafter, referred to as the multidimensional coefficient encoding method).
An example of the individual coefficient encoding method is described in Patent Document 2. In Patent Document 2, a group of LH, HL and HH located spatially at the same position is extracted from the LH subband, the HL subband and the HH subband, and LH, HL and HH are individually encoded into variable-length codes in this order by using Golomb-Rice code.
An example of the multidimensional coefficient encoding method is described in Patent Document 1. In Patent Document 1, a group of LH, HL and HH located spatially at the same position is extracted from the LH subband, the HL subband and the HH subband, and the three coefficients LH, HL and HH are collectively encoded into one code. To be specific, it is determined whether or not LH, HL and HH are zero, and discrimination information of 1 bit for each is generated. Next, the discrimination information are coupled for each group to generate flag information of multiple bit length, and this flag information is encoded into a variable-length code. Thus, a compression ratio when all of the coefficients included in a group are zero in value is increased. However, regarding a non-zero coefficient, the value of the coefficient is encoded into a variable-length code separately.
Another example of the multidimensional coefficient encoding method is described in Non-Patent Document 1. In Non-Patent Document 1, the LH, HL and HH coefficients spatially in neighborhood in the same hierarchy are collected to generate a multidimensional vector and encode it. To be specific, by classifying depending on the electric power of the vector and applying vector quantization depending on the class, the compression efficiency of the coefficient is increased. Further, by eliminating a vector with all coefficients of zero in value as an invalid vector from the encoding target, the compression ratio in high compression with many zero coefficients is increased.    Patent Document 1: Japanese Patent No. 4424522    Patent Document 2: Japanese Patent No. 4650592    Non-Patent Document 1: Matsumura, et al., “Method for Vector Quantization of Wavelet Transform Image by Subband Hierarchy and Electric Power Class” the 10th Picture Coding Symposium of Japan (PCSJ95), pp. 121-122
As described above, as a method for encoding LH, HL and HH located spatially at the same position within the LH subband, HL subband and HH subband belonging to the same hierarchy, there are two methods of the individual coefficient encoding method and the multidimensional coefficient encoding method. There is a two-dimensional signal that a compression ratio becomes higher when the signal is encoded by the multidimensional coefficient encoding method, whereas there is a two-dimensional signal that a compression ratio becomes higher when the signal is encoded by the individual coefficient encoding method. Further, there is a two-dimensional signal which contains in one two-dimensional signal both a part that a compression ratio becomes higher when the signal is encoded by the multidimensional coefficient encoding method and a part that a compression ratio becomes higher when the signal is encoded by the individual coefficient encoding method. Therefore, by a method in which it is defined for an entire two-dimensional signal whether to collectively encode or individually encode a plurality of wavelet transform coefficients of the encoding target, it is difficult to encode at a good compression ratio.